These are fruits in which parts other than the ovary and its wall form an important or conspicuous part of the fruit. Most accessory fruits are simple fruits that have developed from inferior ovaries.. In our gardens, accessory fruits are represented by squash, cucumber, muskmelon, gooseberry, cranberry , and, if you live in the US's deep Deep South, bananas.
The above picture shows a young yellow crookneck squash from my garden, just a tiny bit larger than in real life. The future squash, which here is in inferior ovary, is at the right in the picture. Notice where the sepals are. If the sepals arose from the green stem, or pedicel, then we'd say that the calyx consists of nothing but sepals. But we know from our Standard Blossom that if the sepals are separated from the pedicel there must be calyx material between, so where is the rest of the calyx in this picture? The answer is that in the squash flower the calyx wall fuses with the squash's outside part -- the inferior ovary's wall. Thus the final fruit consists of not only the ovary, but also of an accessory part, the calyx.
By the way, I've torn away part of the the squash-flower corolla so you can see the big, orange stigma. Where are the stamens? Of course this question is a trick, for squash plants have separate male and female flowers. On such plants, a flower with an ovary -- the immature squash here -- must be female, so naturally there would be no stamens to be found! Single-sex flowers are said to be unisexual. A plant bearing unisexual flowers of both sexes is said to be monoecious. Some plants bear only male or female flowers, and those plants are said to be dioecious. Squash plants are monoecious.